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Let k \in \mathbb{Z}^+ and set n=2^k+1. Prove that n is a prime number if and only if the following holds: there is a permutation a_{1},\ldots,a_{n-1} of the numbers 1,2, \ldots, n-1 and a sequence of integers g_{1},\ldots,g_{n-1}, such that n divides g^{a_i}_i - a_{i+1} for every i \in \{1,2,\ldots,n-1\}, where we set a_n = a_1.

Proposed by Vasily Astakhov, Russia

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